Curves and Booleans Woes
I have a method that may help you in this case.

This method works best if you don't have truly vertical surfaces, but there are workarounds to this if you are willing to adopt it in your meshes.

The first recommended step is to take the bottom most surfaces and scale them outward, so that you have a slight slope to your vertical walls.

The next step should solve the rest for you:
This is a fairly long step-by-step, so I chose to link to it from another post here, if this is a problem at all from the moderators, I would be glad to duplicate it here - just let me know.

After you recreate your mesh using the Z-Pass method, you should be able to easily re-scale your bottom most parts of the mesh to get it looking like you intended, if you so choose by applying the displacement modifier, and manipulating the bottom faces to be what you desire.